I have a little experience with sanding and restaining from a few pieces I have done in our home. My initial instinct was to go light and wipe on more stain if I needed to darken it, but I learned that stain also tends to seal, so I wasn't able to get the wood to absorb much more stain after applying the first coat of. I would suggest finding the same or similar wood and testing different shades until you get the results you are looking for. You would need to sand down to bare wood first. And yes, be careful lest you sand through the veneer.
I hired a professional painter to darken some cabinets in a home I was renovating, and he mixed stain into urethane varnish and painted it over the honey oak finish after light sanding (not sanding back to bare wood). The results were surprisingly good. The nice thing about this approach is that it doesn't risk sanding through the veneer, and if you don't get the varnish/stain mix right, you can just wipe it off and try again. Once you are satisfied with the results, seal it with a spray-on varnish.
Resign yourself to the notion that you will never be able to do an undetectable repair. I would say you should not have too much trouble making it look better than it does now.
